An optical system of a laser beam scanner for scanning an original is as shown in FIG. 1. In FIG. 1, a beam emitted from a laser beam producer 11.sub.a diverges into a grating beam B.sub.G and a scanning beam B.sub.P by means of an optical instrument such as a half mirror. The scanning beam B.sub.P is expanded by a beam expander 12.sub.P to have a fixed diameter, and is brought to a galvano mirror 13 to be polarized. After passing through an object lens 14, the scanning beam B.sub.P is reflected at a mirror 15 to scan an original A in the direction indicated by an arrow in FIG. 1. Then each element of a photo-sensor array 16 receives a reflected beam from the original A to convert it into a corresponding voltage signal.
In the meantime, said grating beam B.sub.G is expanded to have a fixed diameter by a beam expander 12.sub.G and is brought to the galvano mirror 13 to be polarized. After passing through the object lens 14, the grating beam B.sub.G is brought to an optical grating 17. Then the grating beam B.sub.G is picked up by each element of a photo-sensor array 18 to produce a grating signal f.sub.in.
In the above described optical system, the galvano mirror 13 is driven by a signal V (Voltage) expressed by an equation: EQU V=V.sub.O sin .omega.t (1)
wherein V.sub.O is the maximum amplitude of the signal V, while .omega. is an angular velocity. Therefore, the swing angle .theta. (radian) of the galvano mirror 13 is expressed by an equation: EQU .theta.=.theta..sub.O sin .omega.t (2)
wherein .theta..sub.O is the maximum swing angle of the galvano mirror.
FIG. 2 shows the detail of the action of the scanning beam B.sub.P which is scanning an original A and is polarized by the galvano mirror 13, from which the mirror 15 is omitted for simplification.
In FIG. 2, the scanning length L (mm) of the scanning beam B.sub.P can be expressed by an equation: ##EQU1## wherein f (mm) is the focal distance of the object lens 14.
On the other hand, the scanning speed V of the scanning beam B.sub.P can be expressed by an equation: ##EQU2## wherein K.sub.1 is K.sub.1 =4.multidot.f.multidot..theta..sub.O .multidot..omega..
It is noted that, assuming that the projection area (diameter) of the scanning beam B.sub.P on the original A is canstant regardless of the swing angle .theta. of the galvano mirror 13, the time T that the spot of the scanning beam B.sub.P on the original A moves per a unit length l can be expressed by an equation: ##EQU3## therefore, the integrated beam quantity E (per a unit time and a unit length) can be expressed by an equation: ##EQU4## wherein P is the intensity (W) of the scanning beam B.sub.P and K.sub.2 is K.sub.2 =l/k.sub.1.
FIG. 3 shows a graph of the variation of the integrated beam quantity E of one scanning line obtained by specifying the parameters of the right member of the equation (6). When an image signal is obtained by using the scanning beam B.sub.P having such a characteristic, the voltage of the signal corresponding to the central portion of the scanning line becomes lower and that of the image signal corresponding to the edge portion thereof becomes higher. Therefore, a compensation process for such a shading phenomenon is carried out in conventional laser beam scanners. To resolve the above-mentioned problem, Japanese Patent laid Open No. 58-27466 discloses the following method. That is, by previously inputting proper shading compensation coefficients for specific points of one scanning line to a memory, an image signal from a photo-sensor is compensated for the shading phenomenon. Inconveniently, this method naturally requires a certain amount of memory capacity, furthermore, since the coefficients for the points other than the specific points are computed through an interpolation process in the method, any system for embodying the method must be provided with computation device and a software for the above computation process. What is more inconvenient of such a computer is its inability of processing image data in real time.
Japanese Patent Publication No. 58-19187 discloses another method as follows. That is, the inverse values of shading compensation coefficients are input to a memory beforehand instead of the coefficients themselves, and an image signal is compensated for the shading phenomenon by means of a multiplication between the coefficient and the image signal. Practically, the inverse coefficients are reduced by a certain value in being input to the memory to allow the memory capacity to be smaller, however, the method has the same drawback that the previous method has.
Japanese Patent laid Open No. 57-119565 discloses yet another method as follows. That is, as well as the above-mentioned two methods, the compensation process is carried out by using coefficients stored in a memory beforehand, in addition, this method adopts a troublesome way of determining the coefficients by previously scanning a reference (white) original.